University of GuilanJournal of Algebra and Related Topics2345-39315120170601A Note on a graph associated to a commutative ring6182239910.22124/jart.2017.2399ENS.VisweswaranSaurashtra UniversityJ.ParejiyaSaurashtra UniversityJournal Article20170806The rings considered in this article are commutative with identity. This article is motivated by the work on comaximal graphs of rings. In this article, with any ring $R$, we associate an undirected graph denoted by $G(R)$, whose vertex set is the set of all elements of $R$ and distinct vertices $x,y$ are joined by an edge in $G(R)$ if and only if $Rxcap Ry = Rxy$. In Section 2 of this article, we classify rings $R$ such that $G(R)$ is complete and we also consider the problem of determining rings $R$ such that $chi(G(R)) = omega(G(R))< infty$. In Section 3 of this article, we classify rings $R$ such that $G(R)$ is planar.<br /><br />https://jart.guilan.ac.ir/article_2399_1591422012d4680950f3bb1760b533a6.pdf